On the shortest path planning for the carangiform robotic fish

Considering the under-actuated characteristic of the carangiform robotic fish whose forward movement and turning are carried out by its single caudal fin, this paper investigates its shortest path planning problem subjected to the terminal constrains. First, a simplified kinematics model is proposed in view of its locomotion characteristic. With this model, the shortest path planning is transformed into the shortest time optimal control problem and the maximum principle is employed to obtain the necessary condition. Furthermore, based on the analysis on the relationship between the length of all feasible paths and the terminal condition, the sufficient and necessary conditions are derived for the shortest path under any terminal constrains. Finally, a program developed with Matlab verifies the effectiveness of the proposed results.